What is "Pattern Theory"?
Pattern-matching is a classical sub-problem of AI systems. Read about the Rete algorithm, or pattern matching in Prolog. Or about Unification. Or about the Warren Abstract Machine. Or about topological data analysis like in GUDHI.
A typical example is the CLIPSrules expert system shell. Or the match expression construct of Ocaml or in Haskell.
In some ways, pattern matching is related to compilers: the GCC compiler (or the Stalin one, or Bigloo, or SBCL) is somehow doing pattern matching on ASTs. So parser generators (e.g. GNU bison, or Iburg) are related to pattern matching.
Patterns also have a different meaning in computer vision.
A classical paper is of course Derivation of a Pattern-Matching Compiler.
A more interesting approach is described in Jacques Pitrat's last book:
Artificial Beings: the conscience of a conscious machine ISBN-13: 978-1848211018
You could also look into Pitrat's blog here.
PS. Jacques Pitrat passed away in oct. 2019.